WORKSHEET – Algebra 1
§9–6, Completing the Square
Name ________________________ Period ____
(First and Last)
Review Problems
1.
r − 10r = 24
2
2.
If x 2 is added to −6x, the sum is 27.
What are the values of x?
6.
An object that is projected straight
downward with initial velocity v feet per
2
second travels a distance s = vt + 16t , where
t = time in seconds. If Andreas is standing in
a hot air balloon 4800 ft. above the ground
and throws a ball straight down with an initial
velocity of 80 ft. per second, in how many
seconds will the ball hit the ground?
3.
2x = x 2 − 3
4.
Find all of the factors of this equation:
15x 2 − 50x + 15 = 0
5.
The height of a triangle is 1 inch greater
than twice its base. The area of the
triangle is 105 square inches What is the
base of the triangle?
b ( 2b + 1)
=A
2
Completing the Square
Example: What quantity should be added to
both sides of the equation to complete the
square for x 2 − 8x = −9?
x 2 − 8x = −9
→ x 2 − 8x = −9
→ x 2 − 8x +16 = −8 + 16
How: Make a hole, then fill the hole with half
of b, squared. In this problem, b is –8; half of
b is –4, and –4 squared is 16. You must add
16 to both sides of the equation. Show steps!
7.
What quantity should be added to both
sides of the equation to complete the
square for x 2 − 12x = 10?
8.
What quantity should be added to both
sides of the equation to complete the
square for x 2 + 2x = −6?
9.
What quantity should be added to both
sides of the equation to complete the
square for x 2 − 16x = 10?
Example: What quantity should be added to
both sides of the equation to complete the
square for x 2 − 10x + 7 = 0?
x 2 − 10x + 7 = 0
→ x 2 − 10x = −7
→ x 2 − 10x +25 = −7 + 25
12.
What is the solution set to the quadratic
equation x 2 + 8x − 48 = 0?
13.
What is the solution set to the quadratic
equation x 2 − 2x = 35?
How: Make a hole by getting rid of the c term
(+ 7), then fill the hole with half of b, squared.
In this problem, b is –10; half of b is –5, and
–5 squared is 25. You must add 25 to both
sides of the equation. Show steps!
10.
What quantity should be added to both
sides of the equation to complete the
square for x 2 + 4x − 2 = 0?
11.
What quantity should be added to both
sides of the equation to complete the
square for y 2 − 18y + 4 = 0?
14.
What is the solution set to the quadratic
equation x 2 + 22x − 75= 0?
15.
What is the solution set to the quadratic
equation x 2 − 2x − 20 = −5?
Example: What is the solution set to the
quadratic equation y 2 − 18y + 17 = 0?
y 2 − 18y + 17 = 0
→ y 2 − 18y = −17
→ y 2 − 18y + 81 = −17 + 81
2
→ ( y − 9 ) = 64
→ ( y − 9 ) = 64
→ y − 9 = ±8
→ y = 9 ± 8
→ y = 9 + 8 and y = 9 − 8
2
→ y = {17 and 1}
16.
What is the solution set to the quadratic
equation x 2 + 6x − 27 = 0?